We consider compact ancient solutions to the three-dimensional Ricci flow that are κ-noncollapsed. We prove that such a solution either is a family of shrinking round spheres or has a unique asymptotic behavior as t → − ∞, which we describe. This analysis applies in particular to the ancient solution constructed by Perelman. © 2020 Wiley Periodicals LLC.

中文翻译：

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三维 Ricci 流的紧凑古代解的独特渐近

我们考虑κ非塌陷的三维 Ricci 流的紧凑古代解。我们证明了这样的解决方案要么是一系列收缩的圆形球体，要么具有独特的渐近行为，如我们所描述的t  → − ∞。这种分析尤其适用于佩雷尔曼构建的古老解决方案。© 2020 威利期刊有限责任公司。